From owner-cypherpunks@toad.com Mon Sep 25 10:50:51 1995 Received: from minbne.mincom.oz.au by orb.mincom.oz.au with SMTP id AA10562 (5.65c/IDA-1.4.4 for eay); Wed, 27 Sep 1995 19:41:55 +1000 Received: by minbne.mincom.oz.au id AA19958 (5.65c/IDA-1.4.4 for eay@orb.mincom.oz.au); Wed, 27 Sep 1995 19:34:59 +1000 Received: from relay3.UU.NET by bunyip.cc.uq.oz.au with SMTP (PP); Wed, 27 Sep 1995 19:13:05 +1000 Received: from toad.com by relay3.UU.NET with SMTP id QQzizb16156; Wed, 27 Sep 1995 04:48:46 -0400 Received: by toad.com id AA07905; Tue, 26 Sep 95 06:31:45 PDT Received: from by toad.com id AB07851; Tue, 26 Sep 95 06:31:40 PDT Received: from servo.qualcomm.com (servo.qualcomm.com [129.46.128.14]) by cygnus.com (8.6.12/8.6.9) with ESMTP id RAA18442 for ; Mon, 25 Sep 1995 17:52:47 -0700 Received: (karn@localhost) by servo.qualcomm.com (8.6.12/QC-BSD-2.5.1) id RAA14732; Mon, 25 Sep 1995 17:50:51 -0700 Date: Mon, 25 Sep 1995 17:50:51 -0700 From: Phil Karn Message-Id: <199509260050.RAA14732@servo.qualcomm.com> To: cypherpunks@toad.com, ipsec-dev@eit.com Subject: Primality verification needed Sender: owner-cypherpunks@toad.com Precedence: bulk Status: RO X-Status: Hi. I've generated a 2047-bit "strong" prime number that I would like to use with Diffie-Hellman key exchange. I assert that not only is this number 'p' prime, but so is (p-1)/2. I've used the mpz_probab_prime() function in the Gnu Math Package (GMP) version 1.3.2 to test this number. This function uses the Miller-Rabin primality test. However, to increase my confidence that this number really is a strong prime, I'd like to ask others to confirm it with other tests. Here's the number in hex: 72a925f760b2f954ed287f1b0953f3e6aef92e456172f9fe86fdd8822241b9c9788fbc289982743e fbcd2ccf062b242d7a567ba8bbb40d79bca7b8e0b6c05f835a5b938d985816bc648985adcff5402a a76756b36c845a840a1d059ce02707e19cf47af0b5a882f32315c19d1b86a56c5389c5e9bee16b65 fde7b1a8d74a7675de9b707d4c5a4633c0290c95ff30a605aeb7ae864ff48370f13cf01d49adb9f2 3d19a439f753ee7703cf342d87f431105c843c78ca4df639931f3458fae8a94d1687e99a76ed99d0 ba87189f42fd31ad8262c54a8cf5914ae6c28c540d714a5f6087a171fb74f4814c6f968d72386ef3 56a05180c3bec7ddd5ef6fe76b1f717b The generator, g, for this prime is 2. Thanks! Phil Karn